LIII. The rectification and observation of signals in the presence of noise

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Abstract
The rectification of random narrow-band noise in the presence of a C.W. or modulated signal is analysed. The detector considered is of the type providing a rectified voltage which is a function of the instantaneous amplitude of the input wave. The smoothing present in the detector circuit is such that the high-frequency components of the applied wave are removed but the low-frequency variations of its envelope are faithfully transmitted. The mean (or D.C.) component of the rectified voltage and its r.m.s. fluctuation about that mean (or L.F. noise output) are calculated as a function of the input signal/noise ratio and particular attention is paid to linear and square-law detectors. The output signal/noise ratio for an amplitude-modulated signal input and for the audible beat reception of a C.W. signal are calculated. The spectrum of the L.F. noise output from a detector supplied with random noise is shown to be closely similar for linear and square-law detectors. The discrimination of a weak signal in noise is shown to be not critically dependent upon the law oi the detector, and in particular the difference for a linear and a square-law detector is negligible. The effect of receiver bandwidth, meter time-constant and integration time in improving the discernment of a weak signal is considered.

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